This invention concerns a procedure for the elimination of interference, such as pulses and linear chirps, in a radar unit of the FMCW type with linear frequency sweep, where the transmitted and received signals are combined to form a useable signal in the form of a difference signal. This difference signal is commonly termed the beat signal, and it includes a wave for each target, where the frequency, amplitude and phase of the wave contain information about the target. The procedure can be used in the field of mobile radar, but it can also be used for other FMCW radar applications.
The principle for linear FMCW radar is well-known, see for example Skolnik, Introduction to Radar Systems, 2nd Ed., McGraw-Hill 1980, chapter 3. Technical advances have resulted in an increased use of FMCW radar units, which will not be considered further here. A linear FMCW (Frequency Modulated Continuous Wave) radar unit, in principle, works as follows:
A frequency sweep controls an oscillator with a variable frequency so that the transmitted frequency varies periodically. Each period has principally three parts, namely a constant base frequency extent, a linear frequency sweep extent and a rapid return to base frequency extent. The linear frequency sweep extent is the time when the radar unit is xe2x80x9ccarrying out useful workxe2x80x9d and often constitutes 70-80% of the total time (work factor 0.7-0.8).
For the sake of simplicity in the discourse below the radar unit and its target are considered stationary. In the case of moving targets or moving radar units the Doppler effect also comes into play. For most actual FMCW systems, however, the Doppler effect only involves a minor correction.
The propagation time from the radar unit to a target and back again is typically a few microseconds. A signal received from a target therefore has the frequency that was transmitted a certain time previously. Since the frequency is swept this is not the same frequency that is being transmitted. The received frequency also has a linear frequency sweep. The received frequency sweep and the transmitted frequency sweep are parallel with a time-displacement equal to the propagation time. Therefore for a fixed target the difference in frequency between the transmitted and received signal will be constant. This constant frequency difference is given by the product of the propagation time to the target and the gradient of the frequency sweep expressed as frequency per unit of time.
Signal processing in a linear FMCW radar unit consists principally of the transmitted and received signals being combined, so that the difference signal (the beat signal) is generated. This signal is the sum of a number of sine waves, where each sine wave represents a radar target. The sine waves have different frequencies, amplitudes and initial phases. Typically a large amplitude corresponds to large target, and a high frequency corresponds to a target at a great distance. The Doppler effect (due to the relative speed) mainly affects the initial phases.
In order to determine what targets are being observed and their sizes and relative speeds, the difference signal is frequency-analysed. The frequency analysis is best carried out digitally. The difference signal is passed through an anti-alias filter and then sampled at a constant sampling rate. Thereafter the sampled signal is multiplied by a window function to reduce the amplitude of the signal at the start and end of the sampling period and the product is sent to a signal processor that carries out a Discrete Fourier Transform, DFT, usually with a fast algorithm, known as an FFT, Fast Fourier Transform. The Fourier Transform is generally complex but for a real time signal (difference signal) it has a certain degree of symmetry. In order to be able to use FFT algorithms the number of samples is usually selected as a power of two (256, 512, 1024 . . . ). 256 samples give 256 FFT coefficients, but if the signal is real the symmetry means that of these 256 values only 128 (actually 129) are independent.
With application of Fourier Transform, for example by FFT, the signal is divided up into a number of discrete frequency components, such as sines. Each frequency corresponds, as indicated, to a distance. The amplitude of a complex FFT coefficient is a measurement of the radar target area (the received power) for the target in the corresponding frequency window (distance window). The FFT performs what is known as a coherent integration of the target signal, which is advantageous. The subsequent signal processing in the system is carried out digitally on the calculated FFT coefficients.
It can be shown that the nominal width of a distance window is inversely proportional to the change in frequency of the linear FMCW sweep during the sampling period. For a distance resolution of 1 m a change in frequency of 150 MHz is required. In order to change the distance resolution, the gradient of the frequency sweep can, for example, be changed while retaining the same sampling time.
The sampling rate limits the frequencies of the beat signal that can be studied and thereby the total observed distance. The width of this xe2x80x9cuseable bandxe2x80x9d that lies parallel to the linear FMCW sweep is often less than 1 MHz.
A linear FMCW radar unit can be subjected to interference if it receives signals other than its own transmitted signals reflected from various targets. The radar unit can be subjected to interference from other radar units, including pulse radar units, pulse compression radar units and other FMCW radar units that are operating at the same time.
A pulse present during the sampling period has a very short extent in the time domain and is very broad-band in the frequency domain. A strong interfering pulse only affects a few samples of the beat signal but can affect all the frequencies or frequency bins in the Fourier Transform. The xe2x80x9cnoise levelxe2x80x9d in the Fourier Transform appears to be increased, so that small targets can be masked by the interference.
A very common form of interference is what is known as a chirp, where the wave form causing the interference moves with a linear frequency through the useable band of the FMCW radar unit. Such chirps are generated by a pulse compression radar unit, and also by another FMCW radar unit if that unit""s transmitted wave form during the base and return extents enters the first unit""s useable band during its sampling period. The third extent, the linear frequency sweep, can also generate a chirp if the frequency sweep of the radar unit causing the interference has a different gradient from the frequency sweep of the first radar unit, e.g. because the radar unit causing the interference has a different distance resolution.
Interference in the form of a linear chirp is always broad-band in frequency, but can also have a considerable extent in time and cause interference to the whole FFT and affect a very large part of the sampled time signal.
There are also short chirps that can hardly be distinguished from pulses. The chirps that are caused by the base extent or return- extent of an interfering FMCW radar unit are of this type.
Interference of short duration such as short pulses or rapid chirps can generally be detected and eliminated in the sampled time signal. and an FFT without interference can then in general be reconstructed. A chirp interference with a large extent in both the time domain and in the Fourier domain can, however, not be eliminated by any simple manipulation of the time signal without negative consequences for the FFT.
According to this invention a procedure is proposed for eliminating interference in radar units of the FMCW type that is capable of eliminating interference with a large extent in both the time domain and Fourier domain. The method according to the invention is characterised by (1) the beat signal being subjected to time-frequency division for time-local resolution, (2) by the interference being detected and eliminated separately in each frequency band individually, after which (3) the time signal free of the interference and its Discrete Fourier Transform, DFT, are calculated from the time-frequency resolution.
The sampled beat signal, the time signal, lies completely in the time domain. The samples give a resolution in time but no resolution at all in frequency. The FFT is a description of the same signal in the Fourier domain. The FFT gives a good resolution in frequency, but no resolution at all in time. Interference, e.g. a chirp, present for a short time is poorly visible in the Fourier domain. Information about the position of the interference is to be found mainly in the phases of the complex FFT values and not in the amounts or amplitude.
What is known as a time-frequency resolution makes it possible to have certain (coarse) resolution of the signal in the time domain and in the Fourier domain. A known time-frequency resolution is the Wigner-Ville Transform, which is what is known as a quadratic transform and therefore creates false cross-modulation products, see Mayer, Wavelets, Algorithms and Applications, SIAM, Philadelphia, 1993. Another known time-frequency resolution is what is known as the wavelet transform, see the book by Mayer, or Rioul/Vetterli, Wavelets and Signal Processing, IEEE Signal Processing Magazine, October 1991, that makes a xe2x80x9cmusicalxe2x80x9d frequency division. The frequency division is into different scalesor xe2x80x9coctavesxe2x80x9d. For high frequencies the frequency resolution (expressed in Hz) is coarser but the time resolution is finer.
The expressions xe2x80x9ctime-frequency analysisxe2x80x9d, xe2x80x9ctime-frequency decompositionxe2x80x9d (cf. the above book by Mayer), xe2x80x9ctime-frequency distributionxe2x80x9d and xe2x80x9ctime-frequency representationxe2x80x9d (cf. the references in the above paper by Rioul/Vetterli) of a signal, leading to a xe2x80x98time-frequency resolutionxe2x80x9d, are all in common use and mean essentially the same thing: some expressions stress the work done (xe2x80x9canalysisxe2x80x9d), other the result of the work (xe2x80x9cdecompositionxe2x80x9d, xe2x80x9crepresentationxe2x80x9d, xe2x80x9cresolutionxe2x80x9d), still other the particular methods used (xe2x80x9cdistributionxe2x80x9d). Here the expressions are used as synonyms.
For the application of interference attenuation in FMCW radar units there is proposed, however, mainly the simplest time/frequency resolution, Short Time Fourier Transform, STFT, described in the Rioul/Vetterli reference above. In STFT the time signal is divided into short sections that can overlap. Each section of signal is multiplied by a window function and a Discrete Fourier Transform is calculated. The STFT provides a frequency decomposition for every small part of the time signal and is a time-frequency decomposition. After the elimination of interference in each frequency band individually, the original time signal is calculated from the STFT. The STFT can therefore usefully contain redundant (overlapping) information.
In this connection it is useful to point out that an FMCW radar unit is the only common type of radar unit where a target corresponds to a standing wave with a certain frequency thus fulfilling the conditions for application of normal Fourier analysis with band-pass filter or DFT (FFT).
Detection of interference in each frequency band can advantageously be carried out by methods suitable for the detection of short duration interference.
In one suitable version of the method, the detection of linear chirps and pulses is carried out by methods for detecting straight lines in images, for example so that interference patterns in the form of straight lines not parallel with the time axis are identified, the times where interference lines intersect the different frequency bands of the STFT are determined and the interference is eliminated separately in each affected frequency band. Methods for detecting straight lines in images are known from image processing, see for example Gonzalez/Woods, Digital Image Processing, Addison-Wesley, 1992. A Hough Transform can be used for the detection of the straight lines.
In another suitable version of the method in accordance with the invention, the beat signal is filtered in association with the time-frequency resolution in narrow frequency bands of the signal in order to increase the sensitivity of the detection. The filter can be determined using adaptive methods. In one favorable version, the filter is applied on one or more of the narrow-band frequency bins of the time-frequency resolution.
In yet another suitable version of the method in accordance with the invention, the beat signal or useable signal is reconstructed after the elimination of interference by extrapolation from samples without interference, in one or more of the narrow-band frequency bands of the time-frequency resolution.
STFT-time-frequency resolution for the detection of interference, the elimination of interference and synthesis of the useable signal has many advantages, particularly for chirps. The advantages consist in general of two characteristics. The first is that a chirp in each frequency bin in the STFT is of short duration and can therefore be detected/eliminated by the same methods as, for example, pulses. The second is that chirps are narrow-band in each frequency band in the STFT and can therefore be described (reduced to zero/extrapolated) using simple polynomials of already known structure.